True, unvaccinated people are being hospitalized at a higher rate and for a longer duration.

However, we are not talking about "the unvaccinated", rather about "a tiny unfortunate fraction of unvaccinated people". There are 4,690 covid patients in ICU beds and 25M unvaccinated people. Assuming all covid ICU patients are unvaccinated, the covid ICU incidence rate within the unvaccinated population is 0.02%.

For an analogy, we could reason that because the prison population skews 90/10 male/female, all males should either undergo a vasectomy, or pay a recurring 10k euro fine. I hope this is obviously unethical.